We propose a history-driven target (HDT) framework in Markov Chain Monte Carlo (MCMC) to improve any random walk algorithm on discrete state spaces, such as general undirected graphs, for efficient sampling from target distribution $\boldsymbolμ$. With broad applications in network science and distributed optimization, recent innovations like the self-repellent random walk (SRRW) achieve near-zero variance by prioritizing under-sampled states through transition kernel modifications based on past visit frequencies. However, SRRW's reliance on explicit computation of transition probabilities for all neighbors at each step introduces substantial computational overhead, while its strict dependence on time-reversible Markov chains excludes advanced non-reversible MCMC methods. To overcome these limitations, instead of direct modification of transition kernel, HDT introduces a history-dependent target distribution $\boldsymbolπ[\mathbf{x}]$ to replace the original target $\boldsymbolμ$ in any graph sampler, where $\mathbf{x}$ represents the empirical measure of past visits. This design preserves lightweight implementation by requiring only local information between the current and proposed states and achieves compatibility with both reversible and non-reversible MCMC samplers, while retaining unbiased samples with target distribution $\boldsymbolμ$ and near-zero variance performance. Extensive experiments in graph sampling demonstrate consistent performance gains, and a memory-efficient Least Recently Used (LRU) cache ensures scalability to large general graphs.

We propose an online learning framework for forecasting nonlinear spatio-temporal signals (fields). The method integrates (i) dimensionality reduction, here, a simple proper orthogonal decomposition (POD) projection; (ii) a generalized autoregressive model to forecast reduced dynamics, here, a reservoir computer; (iii) online adaptation to update the reservoir computer (the model), here, ensemble sequential data assimilation. We demonstrate the framework on a wake past a cylinder governed by the Navier-Stokes equations, exploring the assimilation of full flow fields (projected onto POD modes) and sparse sensors. Three scenarios are examined: a naïve physical state estimation; a two-fold estimation of physical and reservoir states; and a three-fold estimation that also adjusts the model parameters. The two-fold strategy significantly improves ensemble convergence and reduces reconstruction error compared to the naïve approach. The three-fold approach enables robust online training of partially-trained reservoir computers, overcoming limitations of a priori training. By unifying data-driven reduced order modelling with Bayesian data assimilation, this work opens new opportunities for scalable online model learning for nonlinear time series forecasting.

We use a deep learning based approach to predict whether a selected element in a mobile UI screenshot will be perceived by users as tappable, based on pixels only instead of view hierarchies required by previous work. To help designers better understand model predictions and to provide more actionable design feedback than predictions alone, we additionally use ML interpretability techniques to help explain the output of our model. We use XRAI to highlight areas in the input screenshot that most strongly influence the tappability prediction for the selected region, and use k-Nearest Neighbors to present the most similar mobile UIs from the dataset with opposing influences on tappability perception.

A growing number of people engage in online health forums, making it important to understand the quality of the advice they receive. In this paper, we explore the role of expertise in responses provided to help-seeking posts regarding mental health. We study the differences between (1) interactions with peers; and (2) interactions with self-identified mental health professionals. First, we show that a classifier can distinguish between these two groups, indicating that their language use does in fact differ. To understand this difference, we perform several analyses addressing engagement aspects, including whether their comments engage the support-seeker further as well as linguistic aspects, such as dominant language and linguistic style matching. Our work contributes toward the developing efforts of understanding how health experts engage with health information- and support-seekers in social networks. More broadly, it is a step toward a deeper understanding of the styles of interactions that cultivate supportive engagement in online communities.

Commercial high-voltage circuit breaker (CB) condition monitoring systems rely on directly observable physical parameters such as gas filling pressure with pre-defined thresholds. While these parameters are crucial, they only cover a small subset of malfunctioning mechanisms and usually can be monitored only if the CB is disconnected from the grid. To facilitate online condition monitoring while CBs remain connected, non-intrusive measurement techniques such as vibration or acoustic signals are necessary. Currently, CB condition monitoring studies using these signals typically utilize supervised methods for fault diagnostics, where ground-truth fault types are known due to artificially introduced faults in laboratory settings. This supervised approach is however not feasible in real-world applications, where fault labels are unavailable. In this work, we propose a novel unsupervised fault detection and segmentation framework for CBs based on vibration and acoustic signals. This framework can detect deviations from the healthy state. The explainable artificial intelligence (XAI) approach is applied to the detected faults for fault diagnostics. The specific contributions are: (1) we propose an integrated unsupervised fault detection and segmentation framework that is capable of detecting faults and clustering different faults with only healthy data required during training (2) we provide an unsupervised explainability-guided fault diagnostics approach using XAI to offer domain experts potential indications of the aged or faulty components, achieving fault diagnostics without the prerequisite of ground-truth fault labels. These contributions are validated using an experimental dataset from a high-voltage CB under healthy and artificially introduced fault conditions, contributing to more reliable CB system operation.

Existing post-hoc model-agnostic methods generate external explanations for opaque models, primarily by locally attributing the model output to its input features. However, they often lack an explicit and systematic framework for quantifying the contribution of individual features. Building on the Taylor expansion framework introduced by Deng et al. (2024) to unify existing local attribution methods, we propose a rigorous set of postulates -- "precision", "federation", and "zero-discrepancy" -- to govern Taylor term-specific attribution. Guided by these postulates, we introduce TaylorPODA (Taylor expansion-derived imPortance-Order aDapted Attribution), which incorporates an additional "adaptation" property. This property enables alignment with task-specific goals, especially in post-hoc settings lacking ground-truth explanations. Empirical evaluations demonstrate that TaylorPODA achieves competitive results against baseline methods, providing principled and visualization-friendly explanations. This work represents a step toward the trustworthy deployment of opaque models by offering explanations with stronger theoretical grounding.

Given i.i.d.\ samples $X_n =\{ x_1, \dots, x_n \}$ from a distribution supported on a low dimensional manifold ${M}$ embedded in Eucliden space, we consider the graph Laplacian operator $Δ_n$ associated to an $\varepsilon$-proximity graph over $X_n$ and study the asymptotic fluctuations of its eigenvalues around their means. In particular, letting $\hatλ_l^\varepsilon$ denote the $l$-th eigenvalue of $Δ_n$, and under suitable assumptions on the data generating model and on the rate of decay of $\varepsilon$, we prove that $\sqrt{n } (\hatλ_{l}^\varepsilon - \mathbb{E}[\hatλ_{l}^\varepsilon] )$ is asymptotically Gaussian with a variance that we can explicitly characterize. A formal argument allows us to interpret this asymptotic variance as the dissipation of a gradient flow of a suitable energy with respect to the Fisher-Rao geometry. This geometric interpretation allows us to give, in turn, a statistical interpretation of the asymptotic variance in terms of a Cramer-Rao lower bound for the estimation of the eigenvalues of certain weighted Laplace-Beltrami operator. The latter interpretation suggests a form of asymptotic statistical efficiency for the eigenvalues of the graph Laplacian. We also present CLTs for multiple eigenvalues and through several numerical experiments explore the validity of our results when some of the assumptions that we make in our theoretical analysis are relaxed.

Causal inference in longitudinal biomedical data remains a central challenge, especially in psychiatry, where symptom heterogeneity and latent confounding frequently undermine classical estimators. Most existing methods for treatment effect estimation presuppose a fixed outcome variable and address confounding through observed covariate adjustment. However, the assumption of unconfoundedness may not hold for a fixed outcome in practice. To address this foundational limitation, we directly optimize the outcome definition to maximize causal identifiability. Our DEBIAS (Durable Effects with Backdoor-Invariant Aggregated Symptoms) algorithm learns non-negative, clinically interpretable weights for outcome aggregation, maximizing durable treatment effects and empirically minimizing both observed and latent confounding by leveraging the time-limited direct effects of prior treatments in psychiatric longitudinal data. The algorithm also furnishes an empirically verifiable test for outcome unconfoundedness. DEBIAS consistently outperforms state-of-the-art methods in recovering causal effects for clinically interpretable composite outcomes across comprehensive experiments in depression and schizophrenia.

Modern machine learning systems operating in dynamic environments often face \textit{sequential covariate shift} (SCS), where input distributions evolve over time while the conditional distribution remains stable. We introduce FADE (Fisher-based Adaptation to Dynamic Environments), a lightweight and theoretically grounded framework for robust learning under SCS. FADE employs a shift-aware regularization mechanism anchored in Fisher information geometry, guiding adaptation by modulating parameter updates based on sensitivity and stability. To detect significant distribution changes, we propose a Cramer-Rao-informed shift signal that integrates KL divergence with temporal Fisher dynamics. Unlike prior methods requiring task boundaries, target supervision, or experience replay, FADE operates online with fixed memory and no access to target labels. Evaluated on seven benchmarks spanning vision, language, and tabular data, FADE achieves up to 19\% higher accuracy under severe shifts, outperforming methods such as TENT and DIW. FADE also generalizes naturally to federated learning by treating heterogeneous clients as temporally fragmented environments, enabling scalable and stable adaptation in decentralized settings. Theoretical analysis guarantees bounded regret and parameter consistency, while empirical results demonstrate FADE's robustness across modalities and shift intensities.

The discovery of causal relationships is a foundational problem in artificial intelligence, statistics, epidemiology, economics, and beyond. While elegant theories exist for accurate causal discovery given infinite data, real-world applications are inherently resource-constrained. Effective methods for inferring causal relationships from observational data must perform well under finite data and time constraints, where "performing well" implies achieving high, though not perfect accuracy. In his seminal paper A Theory of the Learnable (Valiant, 1984), Valiant highlighted the importance of resource constraints in supervised machine learning, introducing the concept of Probably Approximately Correct (PAC) learning as an alternative to exact learning. Inspired by Valiant's work, we propose the Probably Approximately Correct Causal (PACC) Discovery framework, which extends PAC learning principles to the causal field. This framework emphasizes both computational and sample efficiency for established causal methods such as propensity score techniques and instrumental variable approaches. Furthermore, we show that it can provide theoretical guarantees for other widely used methods, such as the Self-Controlled Case Series (SCCS) method, which had previously lacked such guarantees.